A new reflection x-ray microscope is in the process of final testing. Compared with earlier versions it has a resolving power previously unattainable because of inherent geometrical aberrations and little understood diffraction effects. A "figure" for the optical surfaces has been discovered which eliminates both spherical and obliquity aberrations which can seriously limit the resolution. X-ray lenses, both with and without an axis of symmetry, are under study for possible applications in biomedical research. Local irradiation by x-rays or neutrons of single cells within a small volume and with well defined doses is now a distinct possibility for use in basic studies of radiation damage and repair processes. The increased resolution of the x-ray microscope now makes possible the determination, on a histo-chemical scale, of the atomic constitutents of tissue sections through the use of microradiographs made at two or more wavelengths. Modern electronic detectors and computers would be substituted for the photographic process as they become available.